Problem: How many significant figures does $0.09749000$ have?
Identify the non-zero digits and any zeros between them. These are all significant. $0.0{9749}000$ Leading zeros are not significant. $\color{orange}{0.0}{9749}000$ Since there is a decimal, trailing zeros are significant. $\color{orange}{0.0}{9749000}$ Counting all the significant digits gives us 7.